We study the non-autonomous version of an infinite-dimensional port-Hamiltonian system on an interval $[a, b]$. Employing abstract results on evolution families, we show $C^1$-well-posedness of the corresponding Cauchy problem, and thereby existence and uniqueness of classical solutions for sufficiently regular initial data. Further, we demonstrate that a dissipation condition in the style of the dissipation condition sufficient for uniform exponential stability in the autonomous case also leads to a uniform exponential decay of the energy in this non-autonomous setting.

中文翻译：

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无限维非自治港口哈密尔顿系统的指数稳定性

我们研究了区间 $[a, b]$ 上无限维哈密尔顿系统的非自治版本。使用进化族的抽象结果，我们展示了对应柯西问题的 $C^1$-适定性，从而证明了对于足够规则的初始数据经典解的存在性和唯一性。此外，我们证明了在自主情况下足以实现均匀指数稳定性的耗散条件类型的耗散条件也会导致这种非自主设置中能量的均匀指数衰减。